Cut the chicken into tiny bite-sized pieces. Heat the olive oil in a Dutch oven over medium-high heat. Add the cut chicken and cook for 5-7 minutes, stirring occasionally, until browned on both sides.
Add the diced carrots and diced celery to the browned chicken in the pot. Cook for 3-4 additional minutes, stirring frequently, until the vegetables begin to soften.
Stir in the poultry seasoning or herb and garlic blend. Pour in the chicken broth, cover the pot, and bring to a simmer. Let it cook for 15-20 minutes until the vegetables are tender and the flavors have melded. I like to taste the broth here and adjust the seasoning if needed.
Uncover the pot and pour in the heavy cream. Stir well to incorporate, then return the liquid to a gentle simmer over medium heat.
While the soup simmers, combine the flour, baking powder, egg, milk, dried parsley, and salt in a mixing bowl. Stir everything together until just combined; don't overmix. I always find that handling the dough gently makes the dumplings tender.
Drop spoonfuls of the dumpling dough into the simmering broth. Cover and cook for 5-7 minutes, or until the dumplings are puffed up and fully cooked through. Serve hot and enjoy!